Preheat oven to 350 degrees. Butter and 8 by 8-inch baking dish and line with two sheets of parchment paper, leaving a slight over hang on each side, and butter paper (if you don't care to lift the bars out in one, for easier cutting, you can just butter the baking dish without lining).
In a mixing bowl whisk together flour, graham crack crumbs, baking soda and salt for 20 seconds, set aside. In the bowl of an electric stand mixer fitted with the paddle attachment, blend together butter, brown sugar and granulated sugar until creamy. Mix in egg and vanilla extract. With mixer set on low speed, slowly add in dry ingredients and mix until combined.
Divide dough in half and press one half of the dough into an even layer in the bottom of prepared baking dish. Place chocolate side by side over dough layer. Top chocolate with marshmallow fluff, spreading into an even layer. Take about golf ball size pieces of remaining dough and flatten into small shingles and layer side by side over marshmallow fluff (work to keep any of the fluff from showing through). Bake in preheated oven 27 - 30 minutes until top is lightly golden brown. Cool completely on a wire rack before cutting into squares (use parchment overhang to lift bars from pan before cutting. I recommend cutting just before serving as the filling will being to run a little). Store in an airtight container.